Uniqueness of solutions to the helically reduced wave equation with Sommerfeld boundary conditions

Abstract

We consider the helical reduction of the wave equation with an arbitrary source on (n+1)-dimensional Minkowski space, n⩾2. The reduced equation is of mixed elliptic-hyperbolic type on Rn. We obtain a uniqueness theorem for solutions on a domain consisting of an n-dimensional ball B centered on the reduction of the axis of helical symmetry and satisfying ingoing or outgoing Sommerfeld conditions on ∂B≈Sn−1. Nonlinear generalizations of such boundary value problems (with n=3) arise in the intermediate phase of binary inspiral in general relativity.